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On the general solutions of three functional equations

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The general solutions of the functional equations

$$\begin{aligned} F(pq)= & {} q^\alpha G(p)+p^\alpha H(q)+K(p)L(q),\\ F(pq)= & {} q^\beta G(p)+p^\alpha H(q)+cK(p)K(q) \end{aligned}$$

and

$$\begin{aligned} f(pq)=q^\alpha f(p)+p^\alpha f(q) +cg(p)g(q) \end{aligned}$$

with \(g(1)=0\) and c, a given nonzero real constant, are obtained. Here F, G, H, K, L, f and g are real-valued functions each with domain I, the unit closed interval and \(1\ne \alpha >0\), \(\alpha \in {\mathbb {R}}\); \(1\ne \beta >0\), \(\beta \in {\mathbb {R}}\).

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Correspondence to Dhiraj Kumar Singh.

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Nath, P., Singh, D.K. On the general solutions of three functional equations. Aequat. Math. 96, 325–338 (2022). https://doi.org/10.1007/s00010-021-00801-1

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